"It's not membership of an association - it is a letter whereby a dealer (in securities)
becomes party to an already existing contract between (an)other dealer and an issuer.
There's really nothing more I can give you I'm afraid."
That is more than enough!
Whatever is in the contract is not going to change the translation for "lettre d'adhésion".
The key element is that the new would-be dealer hasn't got much choice. He can only "take it as it is or leave it". Thus it's a "contract of adhesion" [
http://en.wikipedia.org/wiki/Standard_form_contract] and he is joining in by signing a "letter of adhesion".
At a stretch you could also call it a "joining letter".