Formal pairs suit Writing Task 2. Neutral ones work anywhere. Informal ones belong in Speaking.
1.pay attention to
neutralwatch, listen to or think about something carefully
Drivers who do not pay attention to the road cause most accidents.
To, not on; and pay, not give, in this phrase.
Avoid: pay attention on → pay attention to
2.pay the price for
neutralsuffer the results of a mistake or choice
Future generations will pay the price for today's pollution.
A strong phrase for consequences in Task 2.
3.pay tribute to
formalpraise someone publicly
The city paid tribute to the nurses who worked through the pandemic.
Common in news writing.
4.pay a visit to
informalgo to see a person or place
I paid a visit to my old school last summer.
Visit alone is simpler and fine.
5.pay someone a compliment
neutralsay something kind about someone
My teacher paid me a compliment about my pronunciation.
Give someone a compliment is also used.
6.pay taxes
neutralgive money to the government as tax
Everyone who works should pay taxes in proportion to their income.
Pay tax, uncountable, is equally correct.
7.keep in touch with
informalstay in contact with someone
Video calls help migrants keep in touch with family at home.
Stay in touch is an alternative.
8.keep a promise
neutraldo what you said you would
Politicians who fail to keep their promises lose public trust.
Break a promise is the opposite.
Avoid: hold a promise → keep a promise
9.keep pace with
formalmove or develop at the same speed as something
Schools struggle to keep pace with changes in technology.
Keep up with is a less formal alternative.
10.keep track of
neutralfollow and record changes in something
Apps help users keep track of their spending.
Lose track of is the opposite.
11.keep an eye on
informalwatch someone or something carefully
Parents should keep an eye on what their children watch online.
Speaking. Monitor is the formal equivalent.
12.keep fit
informalstay physically healthy through exercise
I keep fit by swimming twice a week.
Natural in Speaking. Stay in shape is similar.
13.keep a secret
neutralnot tell other people something private
Children often find it hard to keep a secret.
Keep, not hold, a secret.
14.catch someone's eye
neutralattract someone's attention
Bright packaging is designed to catch shoppers' eyes.
Eye-catching is the adjective.
15.catch fire
neutralstart burning
Old wiring can make a building catch fire.
No article.
Avoid: catch a fire → catch fire
16.catch a cold
informalbecome ill with a cold
I caught a cold the week before my exam.
Get a cold is also correct.
Avoid: take a cold → catch a cold
17.catch the bus
informalget on a bus in time
I have to catch the bus at seven to get to work on time.
Catch a train and catch a flight follow the same pattern.
18.catch up with
neutralreach the same level as someone ahead of you
Developing countries are trying to catch up with richer nations.
Also means meet a friend again: catch up with friends.