From The TimeSplitters Wiki

TimeSplitters Advance was planned to be released coinciding with TimeSplitters 2, but the game never made it out of development.

FRD has the following to say regarding the game in their IAQ.

"TimeSplitters Advance was a cracking little game actually. There was an awesome Aztec level with loads of monkeys dive-bombing Captain Ash's biplane. We were going to include it in TimeSplitters Future Perfect, but at the last minute it turned out we couldn't be bothered." - FRD

On Graeme Norgate's personal web site, he also mentions that TSA had been completed.

The reason TSA was never released is unknown, though it probably had something to do with lack of resources or licensing problems.