Fetching details from the dictionary...
starting (e.g. of an engine); engaging (e.g. of a lock)
expenses; costs
attack (esp. a corner approach)
barb (of a fish hook)
charge; duty; person in charge; official; clerk
エンジンの掛りが悪くて困っている。
I'm having trouble because the engine is slow to start.
寒い朝は車の掛りが悪くなる。
On cold mornings, the car is harder to start.
鍵の掛りが甘いので修理を頼んだ。
The lock doesn't engage properly, so I asked for a repair.