。
We bought new uniforms to wear for the game.
Literal
We [topic-は] game [at-で] wear new uniforms [object-を] bought.
試合で着る ('to wear at/for the game') is a short relative clause modifying ユニフォーム ('uniforms'). The で here marks the context — 'at the game' — for the wearing. 着る is specifically for upper-body clothing. ユニフォーム is a katakana English loanword.