A veteran was a person who was experienced in a particular background, most often referring to one with prior experience in the military and or combat.
As of 2285, Nyota Uhura was a twenty year space veteran, leaving her Old City Station co-worker confused as to why she chose such an undesirable duty station. She explained that she liked the peace and quiet of her assignment. (Star Trek III: The Search for Spock)
In 2366, Jean-Luc Picard expressed to William T. Riker that if the government of Angosia III survived the night, he would offer them Federation assistance in re-programming its veterans. (TNG: "The Hunted")
The combined Romulan Tal Shiar/Cardassian Obsidian Order fleet that attempted to make a preemptive strike against the Dominion in 2371 was said to be manned by combat veterans. (DS9: "The Die is Cast")
Kira Nerys and members of the Shakaar resistance cell operated during the Cardassian Occupation of Bajor and participated in many combat actions. (DS9: "Shakaar", "The Darkness and the Light", "Ties of Blood and Water")