• make up for something / • make up (to somebody) for something | • make it up to somebody (for something)

• make up for something
-to do something that corrects a bad situation
SYNONYM  compensate
-Compensate for something lost, missed, or deficient.
: (잘못된 상황을 바로잡을 수 있도록) 벌충[만회]하다
e.g.)
Nothing can make up for the loss of a child.    그 무엇도 잃어버린 자식을 대신할 수는 없다.
After all the delays, we were anxious to make up for lost time.
    그 모든 지체들이 있은 후에 우리는 잃어버린 시간을 만회하기를 간절히 바라고 있었다.
Her enthusiasm makes up for her lack of experience.    그녀의 열의가 그녀의 경험 부족을 벌충한다.
A warm and sunny September made up for a miserable wet August.
‘he was eager to make up for lost time’


• make up (to somebody) for something   |   • make it up to somebody (for something)
-to do something for somebody or give them something because you have disappointed them or caused them trouble and wish to show that you are sorry
SYNONYM  compensate
-Compensate someone for negligent or unfair treatment.
: (손해나 잘못을 야기한 것 등) ~에 대해 (에게) 보상하다
e.g.)
How can I make up for the way I've treated you?
    어떻게 해야 내가 당신에게 한 처사에 대한 보상이 될까요?
(informal) I'll make it up to you, I promise.     (비격식) 내가 당신에게 그에 대한 보상을 하겠어요. 약속해요.
‘I'll try to make it up to you in the future’
George wanted to make it up to Andrea for being so bad-tempered towards her earlier.

Ref)
You cannot change the word order in "make it up" that I can see; it has to be "make it up to [someone]".
https://forum.wordreference.com/threads/the-difference-between-make-up-for-something-and-make-it-up.3706044/

cf)
• make up to somebody
-(British English, informal, disapproving) to be pleasant to somebody, praise them, etc., especially in order to get an advantage for yourself
-Attempt to win the favour of someone by being pleasant.
: (~에게) 알랑거리다
e.g.)
‘you can't go on about morals when you're making up to Adam like that’
‘I bet she was making up to the master.’
‘Harry made up to her shamelessly.’

https://forum.wordreference.com/threads/make-it-up-to-somebody-for-something-make-up-for-something.3738587/