retrench vs bring down

retrench and bring down both are verbs.

Word	Noun	Adjective	Verb	Adverb
retrench	No	No	Yes	No
bring down	No	No	Yes	No

As verbs, bring down is a hypernym of retrench; that is, bring down is a word with a broader meaning than retrench:

Other hypernyms of retrench include cut, cut back, cut down, reduce, trim, trim back, trim down.

retrench (verb)	bring down (verb)
make a reduction, as in one's workforce	cut down on; make a reduction in
tighten one's belt; use resources carefully	impose something unpleasant
	cause to be enthusiastic
	cause to come to the ground
	move something or somebody to a lower position
	cause the downfall of; of rulers