At present Commonwealth citizens, who do not also hold a valid UK passport, resident outside of UK must first live legitimately in UK for five years immediately prior to applying and have indefinite right to remain on their passport. They must also have a work (not student) visa. In addition different jobs have different Nationality criteria.
In recent years we've recruited about 50 Commonwealth citizens, resident overseas and granted residency waivers. At present no plans have been announced for this year, but typically when it does happen the nationality/residency eligibility criteria will announce the change for a limited period on the RN website. Last year we received about 16-20 applications for each of the 50 posts available. Trouble is that due to Brexit, it gets a bit difficult for the Foreign & Commonwealth Office to permit Commonwealth citizens taking-up employment to enter UK, but then trying to explain to EU citizens that in future they maybe cannot live in UK. Interesting times.
Bottom line? Choose a job that appeals, then watch this space with regard Nationality and Residency eligibility:
https://www.royalnavy.mod.uk/careers/joining/get-ready-to-join/royal-navy-rating/am-i-eligible
Best of luck.