Word for "under the support/help and protection of"

"Connivance", which has more pejorative overtones than some other options, is probably your best bet.

OED

connivance, n.1. a. The action of conniving; the action of winking at, overlooking or ignoring (an offence, fault, etc.); often implying secret sympathy or approval: tacit permission or sanction; encouragement by forbearing to condemn.

1861 "G. Ross W. Bell's Dictionary of the Law of Scotland" (rev. ed.) 297 The husband's connivance in her guilt..is a good defence to the wife against an action of divorce.

"... homes of a particular community vandalized with the connivance of the police."

"Aegis" I believe is the proper word.

https://www.merriam-webster.com/dictionary/aegis