Anscombe's tenure at the Irish region came to an end at the end of the 2013/14 season, with Les Kiss taking on the interim director of rugby role at the Kingspan Stadium.
After opening up with a dramatic 32-32 draw away to the Scarlets, Kiss and Ulster earned their first win of the GUINNESS PRO12 season at home to Zebre last time out.
And No.8 Williams is confident his side are strong enough to deal with the change and move forward in what is now a new era at the club, with Kiss also due to depart for pastures new in the next few weeks to return to full-time duties as assistant coach of Ireland.
"We are a strong bunch of lads and a strong group. It just goes to show the character that has been built here over the last five or six years with whoever has come in or gone," Williams told BBC Sport Northern Ireland.
"It is a cutthroat world as players we get cut and it goes to the management as well. People move on and that is how rugby is but in-house we stick together and there is a strong bond.
"With the pre-season games and the first two games of the season he [Les Kiss] has just brought a different aspect.
"He is a very attention to detail type of coach and has been a breath of fresh air. I have enjoyed it, I get along well with him and he has brought a lot of different ideas to the team in areas where we may have struggled in the last couple of years."
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