Before you call a general handyman, figure out what's actually broken, because that changes who you want. A cracked pane or fog between the two panes of a double pane window is a job for a local glass shop. They can swap just the sealed glass unit and leave the frame in place, which usually costs less than a new window. Old wood windows with broken sash cords or soft, rotted sills are carpentry, and a handyman who does trim work can handle those.
Property managers in your area are a good source for names, since they keep vendor lists for exactly this. You're right to get it fixed now. A broken window turns into a water or security problem fast on a rental.
What city is the property in? Locals here can name shops they've used.