As far as I am aware of, there is no formal diplomatic ties between Singapore and Nepal even if Nepal has a mission based in Singapore.

Secondly, (please correct me if I'm wrong) Singapore Police Force does not directly recruit Gurkhas but instead, the selection of Gurkhas are done by the British camp. A portion of them are then later on "seconded" to Singapore and led by a British officer. Singapore used to be a colonial slave of British so even after post-independence, Singapore has retained very much the colonial attitude in its dealings.