Meaning trap
give up
surrender to authorities
To formally surrender oneself or someone else to the police or another authority, often after being sought or pursued.

Don't mix these meanings
Same phrase, different job.
To formally surrender oneself or someone else to the police or another authority, often after being sought or pursued.
'give up' also has the more basic meaning 'stop trying'; this is the advanced sense.
Hear it in context
Notice where the phrase sounds natural.
After weeks on the run, the suspect finally gave himself up to the police.
In some cases, fugitives choose to give themselves up rather than face the stress of constant pursuit.
Fix the pattern
One small grammar move makes it sound right.
Not: He gave up to the police.
Say: He gave himself up to the police.
This sense needs a reflexive object: 'give yourself/himself up'. Bare 'give up' means quit.
Which sounds natural?
Tap the one a native speaker would say.
'Give yourself up' is the natural phrasing for surrendering. 'Surrender oneself to the authorities' is legalistic.
Build natural chunks
Words that usually travel with it.
give + oneself + up
- himself up
- themselves up
- the suspect up
- to the police
Don't confuse it
Related
Other meanings and phrases to compare.
- give up (stop trying) — 'give up' also has the more basic meaning 'stop trying'; this is the advanced sense.