is there NAT in IPv6 for private-to-public translation like in IPv4. I know that there is a protocol translation between v4 and v6 but did not find anything about same protocol translation . Thank you !
There's a multitude of IPv4-to-IPv6 transitioning mechanisms - for an overview check WP:IPv6 transition mechanism.
IPv6 is normally deployed (and should be) with local and public IP addresses simultaneously, and when done correctly there's no need for NAT.
NAT is a kludge to work around the fact that the IPv4 address space is too small and the initial allocation plan far too generous (simply, nobody could foresee the demand before the WWW). With IPv6 there should be no problem getting an address allocation that fits your needs from your ISP.
However, if required, IPv6-to-IPv6 Network Prefix Translation can be used in a similar way to IPv4 NAT.