British English has many approving phrases for leaving people to do their work.
To give someone a free hand: To let someone decide how to do a job.
To give someone free rein: To give someone wide freedom to act.
To let someone get on with it: To stop checking and let the work proceed.
Why keep a dog and bark yourself?: There is no point in paying someone to do a job and then doing it yourself. The proverb is recorded from the late sixteenth century.