keep shtum

cobbler, keep to your last

One should not criticise matters outside one's field of expertise; one should mind one's business.

earn one's keep

To perform satisfactory physical labor or to provide other worthy services in return for remuneration, lodging, or other benefits; to support oneself financially.

keep a civil tongue in one's head

To maintain a polite manner of speaking.

keep a close watch

to pay careful attention to a situation or a thing, so that you can deal with any changes or problems.

keep a cool head

To keep one's cool; to stay calm.

keep a lid on

To keep something secret.

keep a low profile

To be discreet and quiet.

keep a weather eye open

to maintain a background awareness of something; to remain alert to changes without it occupying one's full attention.