Hana would've mostly stuck around NYC (where 'around' refers to several surrounding states as well as the city proper) up through 2011. As long as she could assist in taking out Company and Humanis First types. Legally or illegally, Hana wouldn't particularly care; ergo, she may have worked with any number of people on such errands, in a sort of loose collaboration, and in other cases may've just left the cleanup as their problem.
After the Columbia bombing and ensuring Helena et al. had a suitable honor guard for their respective afterlives, Hana took off for Israel. Pinehearst being public and officially sanctioned and having a great deal of clout both above and below the board, she decided to apply her skills towards more manageable enemies — and the Middle East always has terrorists. Teo came with. Eve happened along a little while later. Sometimes they worked in collaboration with the Israeli government (or others), and sometimes they just did whatever they saw fit. Both of her cohorts ultimately returned to the States (independently), but Hana's still out there.
Hana keeps in touch, to the extent that anyone who knows Wireless can send her a message and expect a prompt reply. Sometimes she does favors for old acquaintances. She's still not much for small talk, and never got into the Christmas card habit. Never did correct her 'official' identity, either — Hana Gitelman hasn't existed as a part of any record system since around about October 2005, and she doesn't see a reason to change that.