A lot of Asian airlines, for example, have British, Australian and New Zealand crews, among others. SQ has crews from a number of nationalities. Following the pilots strike in Australia some years ago, the flight crew announcements started coming over in European and American accents, and still did, on Ansett anyway, until very recently. Air Pacific used QF crerws until local crews took over, etc., etc.
I think most national carriers would probably like to employ predominantly local crews, but, depending on the size of the airline, it's not often a realistic proposition, at least in the short term. I imagine it's not an issue in countries such as the USA, Britain, etc.?
"...every aircraft is subtly different.."