がついて

is attached; comes on; is acquired

→ が
phrase Rare #33,317
is attached; comes on; is acquired This is the て-form of つく with が. Depending on the noun, it can mean that something is attached or included, a light or warning comes on, contact is made, or a quality or habit is acquired.
JA: この車にはカーナビがついています。
EN: This car has a navigation system included.

やっとあなたに連絡がついてよかった

I'm glad I finally got in touch with you.

一度でも勝てる自信がついていいんだけれど

It would be nice if I could win even just once—it would give me confidence.

一度悪い習慣がついてしまうそれを取り除くのは難しい

Once you develop a bad habit, it’s difficult to break it.

ガソリンランプがついてからどれくらい走れる

How far can you drive after the gas light comes on?

よいがついていれば家の価値を高めるでしょう

Having a nice garden would add value to the house.