To Be Employed At
To Work For
transitive verb, ichidan verb
The kanji is work which means this verb has something to do with working. It's not straight up "to work," instead it's "to work for" or "to be employed at."
つとめる
The reading is the same as the other word that means "to work for" (務める). Remember this and you'll be able to remember the reading for this word too.
娘が小学校に上がったので、私は図書館に勤め始めました。
I started working at a library ever since my daughter got into primary school.