Can I apply for VA disability compensation for a disease or injury diagnosed after service? Short Answer Yes you can. Read on.
Service connection may be established for a disability resulting from diseases or injuries which are clearly present in service or for a disease diagnosed after discharge from service, when all the evidence, including that pertinent to service, establishes that the disease was incurred in service.  38 U.S.C.A. §§ 1110; 38 C.F.R. §3.303:
Establishing service connection generally requires medical, or in certain circumstances, lay evidence of

1. a current disability; 
2. an in-service incurrence or aggravation of a disease or injury;
3. and a nexus between the claimed in-service disease or injury and the present disability.

References
Title 38 C.F.R. 3.303
Title 38, C.F.R, 3.309(a)
Title 38, C.F.R, 3.307(a)(2) and (a)(3)
Davidson v. Shinseki, 581 F.3d 1313 (Fed. Cir. 2009).  That an injury or disease occurred in service is not enough; there must be chronic disability resulting from that injury or disease.  If there is no showing of a resulting chronic condition during service, then a showing of continuity of symptomatology after service is required to support a finding of chronicity.  
38 C.F.R. § 3.303(b).  The Federal Circuit recently held that continuity of symptomatology under 38 C.F.R. § 3.303(b) applies only to chronic diseases listed in 38 C.F.R. § 3.309 (2015).  Walker v. Shinseki, 708 F.3d 1331, 1338 (2013).  Additionally, for veterans who have served 90 days or more of active service during a war period or after December 31, 1946, certain chronic disabilities are presumed to have been incurred in service if manifest to a compensable degree within one year of discharge from service.  38 U.S.C.A. §§ 1101, 1112, 1113, 1137 (West 2014); 38 C.F.R. §§ 3.307, 3.309 (2015).

Diseases Within One-Year Post-Service

VA presumes service connection for certain diseases even though they were not present during military service. Some of these diseases in which presumptive service connection may be granted include hypertension, arthritis, diabetes mellitus, and peptic ulcers. A complete list of diseases is in Title 38, Code of Federal Regulation, 3.309(a).

 

The post-service disease must be at a compensable degree (i.e., 10% or more disabling) within one year after the date of separation from service, with certain exceptions. The regulation that governs eligible service dates for diseases that occur within one year after separation from service is in Title 38, Code of Federal Regulation, 3.307(a)(2) and (a)(3).

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DAVIDSON v. SHINSEKI, 581 F.3d 1313 (Fed. Cir. 2009)

Michael D. Austin, Trial Attorney, Commercial Litigation Branch, Civil Division, United States Department of Justice, of Washington, DC, for respondent-appellee. With him on the brief were Tony West, Assistant Attorney General, Jeanne E. Davidson, Director, and Kirk T. Manhardt, Assistant Director. Of counsel on the brief were David J.

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Walker v. Shinseki, 708 F.3d 1331 (Fed. Cir. 2013)

David S. Forman, Finnegan, Henderson, Farabow, Garrett & Dunner, LLP, of Washington, DC, argued for claimant-appellant. With him on the brief was Anita Bhushan, of Atlanta, Georgia. Of counsel on the brief were Louis J. George and Barton F. Stichman, National Veterans Legal Services Program, of Washington, DC.

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Diseases Within One-Year Post-Service

• You must be a Veteran who was discharged under conditions other than dishonorable.
• You must have a disease that is at least 10% disabling within one year after separation from service
• The disease must be among those listed in Title 38, Code of Federal Regulation, 3.309(a)

• Hansen’s Disease must have appeared within three years after separation.
• Tuberculosis must have appeared within three years after separation.
• Multiple sclerosis must have appeared within seven years after separation.
• Amyotrophic Lateral Sclerosis (ALS), also known as Lou Gehrig’s Disease any time after separation from service

• The evidence must show that the disease is at least 10 percent disabling. (An example is you’re taking medication for hypertension.)
• The evidence must show the disease appeared within the time limits shown above.

• Apply online using eBenefits, OR
• Work with an accredited representative or agent, OR
• Go to a VA regional office and have a VA employee assist you. You can find your regional office on our Facility Locator page.

Source: Diseases Within One-Year Post-Service

Author: Tbird