。
Please give my very best regards to that person.
Literal
That person [to-に] repeatedly-earnestly well-regards.
あの方 (あのかた) is the polite 'that person.' くれぐれも 'earnestly / repeatedly / with great care' strengthens the request. よろしく is the standard set phrase for 'regards / please treat them well.' The whole expression is a formal, polite farewell request — 'please convey my best wishes.'