pick up a fight: is it correct?
The dictionary only says pick a fight with someone, although I read some say pick up a fight.
Many thanks for your time!

Question

pick up a fight: is it correct?
The dictionary only says  pick a fight with someone,  although I read some say pick up a fight.  
Many thanks for your time!

Answer

'Pick a fight' is the correct term. 'Pick up a fight' makes no sense.

Answer

You can "pick up where you left off"
So if you want to say this: "Pick up the fight where you guys left off!" You can. But simply saying "pick up a fight" makes no sense.

Answer

You've confused the two definitions of pick :)
Pick can mean to poke/scratch at something. It could also mean to lift/carry something up. To pick a fight is figurative language but the first definition is still correct.

Answer

"Pick up a fight" doesn't exist as a fixed expression.  "Pick a fight" is correct