The most general term is service life. However, the usual one for aircraft engines is TBO - time between overhauls (often interpreted as "time before overhaul", too). The time left before the next overhaul can be designated as "remaining TBO", although the usual way in aviation is to indicate the time since last ovehaul (TSO, or TSOH, or SMOH, or TSMOH, M stands for "major").

--------------------------------------------------
Note added at 16 mins (2011-10-01 10:56:50 GMT)
--------------------------------------------------

Oh, and it's never expressed in kilometers, it's flight hours only. Sometimes, there are additional limitations on years in operation and/or start cycles. For example, on my aircraft it's 2000 flight hours or 12 years, whichever comes earlier.