Shrink was a 20th century Earth slang term for a psychiatrist, psychoanalyst, psychologist, or therapist in general.
In 2259, La'an Noonien-Singh saw Doctor Sanchez aboard the USS Enterprise and referred to him as a head shrinker. Una Chin-Riley was glad that Noonien-Singh was making use of Starfleet recovery assistance. (SNW: "All Those Who Wander ")
In 2364, after Deanna Troi introduced herself as the USS Enterprise-D's ship's counselor, Clare Raymond referred to her as "the local shrink". When Troi indicated her unfamiliarity with the phrase, Raymond waved it off. (TNG: "The Neutral Zone")