Our school district has a strong music program, which my kids have enthusiastically embraced. The individual teachers generally give out a packet of contact info for people providing private lessons. The teachers give this out at the end of the school year, to encourage students to continue over the summer break (and include upper level students to help younger beginners). Try to contact the school system to reach the appropriate instructors, to add your name to the list.
Instrument sale/rental/repair businesses may also act as a link point for private lesson referrals.
Other ideas: substitute teacher for the music instructors, accompianist for choral groups or solos like All-County/All-State, pit for school or local musicals.
We are pretty busy all year with school music stuff. There are 3 All-County weekends from January through February, and our youngest 2 boys at home are each in one. Musical is in 3 weeks, so pit practice begins ramping up in frequency for DS4. Spring concerts for each, followed by Houghton String Festival in May, and Recital usually in June for DS4 thru his private cello teacher. There's also the random "Will you play taps on Memorial day?" things, too. So school opens up lots of opportunities.