Well, not really trust.. More like he acknowledges Gin as someone worthy of his presence..

Some extra details:

Zomari yells that since when do Shinigami have the right to decide what's evil or not.. That it's just the Shinigami's conceit who decided that Hollows are evil, and that's the reason why Byakuya is going to kill him now.. Suddenly Byakuya interrupts him, and says.. "At what time have I said that I will cut you as a Shinigami..? The only reason I slash you is that you've...".. he thinks of Rukia being controlled.. "pointed your blade towards my pride."
Oh~, some sibling love.. =p Also Isane will heal Hanatarou and Rukia..

source: animenewsnetwork

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