It is indeed used this way. Tennis provides us quite a few since it is such a “mental sport”, as indeed is the focus of the book where we find (emphasis mine in all examples):
Nevertheless, Djokovic was soon up 4–1 and had chances for a second “insurance” break on Federer’s server. But he tightened up again, missed, and Federer held. (Allen Fox, Tennis: Winning the Mental Match, 2010)
And when he was attempting to execute them, the outcome wasn’t very pleasant. He tightened up in my opinion. And as a result, he failed to get much pace on the second serves he did get in. (Andy Murray’s Mistakes Against Federer In The Australian Open Final!, 2010)
There are plenty of cases from other sports:
The talented freshman was nervous. So much so, that he tightened up and didn’t deliver his best, failing to carve his way through the 145-pound bracket. (Jeremy Elliot, Cumberland Valley freshman Felix Belga reaches the quarterfinals of the King of the Mountain Wrestling Tournament, 2012).
Explaining Owen’s losses to Peacock, Neil wrote, “It is significant that Jesse showed, very plainly, that he was putting out a lot more energy—nervous energy in the form of tension—in losing than he had in his winning races. The pictures show it. He’s tightened up, laboring, as he finishes a foot or so behind Peacock…”. (Jeremy Schaap, Triumph:
The Untold Story of Jesse Owens And Hitler’s Olympics, 2007).
In fiction we can find examples, including some more from sport:
In desperation Luke finally sent in Larry Akers to pitch. At first he tightened up and stopped the winning streak of Morningside, and then, he, too, fell by the wayside, and the hooting, yelling crowd had his “Angora,” as Peaches dolefully remarked. (Lester Chadwick, Baseball Joe on the School Nine, 1912)
And that are not:
“What?” He tightened up; noticably nervous. (“YenamMan”, “Relative Dimensions”)
Two things lead to it being less common than loosen up.
- As the line between the two is that loosened up is the appropriate lack of nerves, and tightened up the degree of nerves that will cause problems, loosen up is positive and appears often in the imperative, while tighten up is negative and doesn't.
- Tighten up is also used of “tight” performance without sloppiness or errors, a sense that will appear in the imperative, and hence tightened up needs qualification to ensure we get the understand the correct sense.