"Hold down" is a phrasal verb that means to keep something or someone under control or to maintain something at a low level. There are several synonyms for this term, depending on the specific context.
Some synonyms for "hold down" include "restrain," "keep in check," "suppress," "control," "repress," "subdue," "dominate," "govern," "keep under wraps," and "keep a lid on." Other alternatives include "contain," "curb," "restrict," "limit," "regulate," "manage," "moderate," and "keep a grip on."
Regardless of which synonym is used, the meaning is the same: to exert control over something or someone, either through physical force or through mental or emotional means.