Kulkarni was commissioned a midshipman in the Royal Indian Navy on 1 September 1940.[2] As a gunnery officer on HMS Glasgow, he was involved in a friendly fire incident on 7 December 1941 in which Glasgow sank the patrol vessel HMIS Prabhavati, having mistaken it for a submarine.[3] He was promoted acting sub-lieutenant on 1 May 1942, having undergone gunnery and navigation courses at Portsmouth.[4] He was assigned to the minesweeper HMIS Carnatic on 19 October 1942,[5] and was promoted lieutenant on 1 July 1943.[6] On 22 July, he was posted to the sloop HMIS Hindustan.[7]
Kulkarni was promoted acting lieutenant-commander on 31 December 1948,[8] and to substantive lieutenant-commander on 1 July 1951.[9] Specialising in radar and advanced navigation, he qualified in various advanced courses in the United Kingdom, along with the National Defence College course.[10] On 15 February 1955, he was promoted acting commander and appointed Executive Officer I.N. Barracks, Bombay,[11] with promotion to the substantive rank on 31 December.[12] He successively commanded the frigate INS Trishul and the destroyers Rajput and Rana.[10] Promoted captain, he commanded the 15th Frigate Squadron from 1961 to 1963.[13] He then served as Director National Cadet Corps for Gujarat for a year, and was appointed Naval Officer-in-Charge, Goa in 1964.[10] He was promoted commodore and appointed Assistant Chief of the Naval Staff in 1967.[10]