Depends. Onscreen, we can only establish that TMP can't have taken place earlier than late 2272 (because Kirk hasn't been logging star hours for 2.5 years, and Kirk's five-year mission ended during the year 2270 as per VOY dialogue). We can't establish the last possible date for TMP very well, except of course as "before TWoK".
There's also a line spoken by President Jaresh-Inyo in "Homefront" stating that there hadn't been a Starfleet emergency in nearly a century with the exception of the Borg incident. It's not clear if he's referring to V'Ger as he could be talking about the events of TVH, as well. But it's certainly possible that he could be referring to events one hundred years in the past when dealing with a crisis in 2372.
We have indirect evidence, but not much of it. At least some starships adopted the new red wraparound uniform jackets by 2278, as per TNG "Cause and Effect", so it would be odd if Earth and the Enterprise (both central to the Federation and thus likely to receive hot new fashion very fast) continued to wear the TMP wardrobe after that date. However, TMP dialogue also says Voyager Six disappeared more than 300 years before the events of the movie, and in the real world the first Voyager was launched no earlier than 1977.
We also see personnel from other Starfleet installations wearing similar uniforms during TMP, but there's no sign of the TWOK uniforms. Kirk was wearing an admiral's uniform before boarding Enterprise
due to his having served as CSO prior to TMP, and Commander Branch and his staff at Epsilon IX
wore uniforms much like those worn by the Enterprise