Another word for improve
To make better
better, ameliorate, mend, amend, enhance, enrich, cultivate, revise, update, upgrade, elevate, polish, refine, purify, enlarge, touch up, edit, emend, civilize, educate, meliorate, landscape, develop, revamp, renew, give color to, set right, reorganize, promote, reform, raise, lift, rectify, correct, rehabilitate, renovate, spruce up, gentrify, refashion, regenerate, retread, overhaul, fix, straighten out, distill, change for the better, fix up*, doctor up*, give a good going over*, be the making of*; see also adjust 3, change 1, correct 1, repair.
To become better
get better, advance, progress, make progress, show improvement, make strides, make headway, gain ground, ameliorate, regenerate, renew, recover, gain strength, develop, grow better, grow, rally, mend, gain, come around, profit, augment, widen, increase, mellow, mature, come along, come on, get on, get along, take a new lease on life*, look up*, shape up*, pick up*, perk up*, snap out of it*; see also recover 2, 3.
improve and better both imply a correcting or advancing of something that is not in itself necessarily bad, the former by supplying a lack or want to improve a method and the latter by seeking something more satisfying he's left his job to better himself; ameliorate implies improving to some degree a condition that is bad, oppressive, or intolerable to begin with to ameliorate the lot of the poor