Scott Boyd, 27, was found dead at home by their mother Maureen in Auchinleck, Ayrshire on Wednesday.
Clark expressed his sympathy on behalf of everyone at the club and will leave it up to the 33-year-old former Rangers striker to decide whether he wants to play in the Ladbrokes Premiership game against Dundee at Dens Park on Saturday.
“It has been tough for the football club since we learned the news on Wednesday morning,” he told Press Association Sport.
“Our supporters, the board and everyone connected with the football club send their deepest condolences to Kris and his family.
“I addressed the players on Wednesday and Kris came in today and addressed the players.
“It was emotional for everybody. It was emotional for me, the staff, for the players because we are very close.
“It was a delivery of a speech from a very strong character, a very experienced man.
“Him and his family have had an horrendous few days and it was very emotional but it shows me that the group has a tremendous togetherness and we will stay strong for him.
“Whatever Kris needs, we will support. We will be there every step of the way, whatever is needed.
“I have been speaking to Kris since the horrendous news and it will be left up to him, it is his decision, whether playing or training. I will be guided by him.
“The best tribute to Kris, his family and his late brother, that we can go there (Dundee), put on a performance and get the win.
Midfielder Greg Kiltie could be out until after the October international break after suffering a recurrence of a hamstring injury.
Rory McKenzie is back following a thigh injury and Scott Boyd, who joined on loan from Ross County until the end of the season, is in the squad while Greg Taylor serves the first part of a two-game ban with long-term injured Miles Addison (ankle) and Callum McFadzean (foot) still out.