Some tips for hiring audio contract work

Allocate beforehand a couple days for checking the submissions. When evaluating the work of musicians and sound designers, you will probably need to listen to several songs in different styles, watch videos with their audio replacement for existing games, check their bandcamp and soundcloud tracks, etc.
It can take easily half an hour to check the portfolio from a prolific composer. Multiply that by the number of candidates, and you can see how time will slip through your fingers.

Music (and art in general) is difficult to define with words. Use metaphores, analogies and comparisions. Say how you would like the player to feel when listening to the music, or hearing a particular effect. Should the player feel relaxed, anxious, intrigued? Point out to other games that generate the same ambience or that have a similar style to what you are looking for. Mention what exactly makes them similar, what you like and what you don't.
If you have any, mention concrete wishes or preference about the music, like which instruments would you prefer, tempo, rythm, etc. And especially mention things that you don't want. Do you hate chiptunes, but would consider Drum & Bass for the music? Say it.

Include as much technical details as you can on the pieces you need. How many songs or effects? How and where each will be used? Desired length, if they will be looping, and any other detail will help the contractor in their estimation. Are using or willing to use middleware like FMOD or Wwise to make the audio adaptive? Which game engine you are using?
Several musicians who focus on games also have exprience using the most popular engines, like Unity or UE, which can make the workflow easier.

Specify additional requirements both about the work and the contractor. Do you need the rights to the music? Are you ok with using existing audio? Would you like them to have previous experience in the particular game genre? Are you willing to work with agencies, or would you only work directly with the musicians? Do you want to sign a contract? Do you want to work only with people in your country or your same time zone?

Mention a budget if you have one, or ask for rates. Some musicians are flexible about this, but it's good anyway to ask for what they would like, as it might allow you to both realistically evaluate your budget and make reasonable proposals to them. And do not forget to mention milestones or launch dates if you have already defined them.