The 30-year-old struggled during the latter part of this past season for the Scottish Premiership side.
The midfielder was largely disappointing during the latter half of this past season as he appeared to return from injury too quickly to try and help the Bhoys see off Aberdeen's title challenge.
And while Ronny Deila's men were able to win the Scottish Premiership once again, Brown's form has been earmarked as an issue that the Norwegian's successor will have to tackle.
But Boyd is confident that Brown will soon be back to his best, and pointed out that Rangers' acquisition of 33-year-old Joey Barton proved that the Scotland international had several years at the top ahead of him.
"He's 30 just now but a team across the city are signing players who are older than Scott," he told the Evening Times. "So he has a few years' advantage. Scott has great experience, he's our captain, blighted by injury a little bit last season but he knows he has to be pushing to get back to full fitness.
"It depends on Brendan's philosophy is, what his type of football will be, what his formation will be but I'm sure Scott will have loads to offer both on and off the park."
The former Hibernian man will surely benefit from the summer months as they will allow him to fully recover from any injury worries that he had during the remaining weeks of the campaign.
And with some writing him off getting back to the level he once was, Brown will surely be relishing the opportunity to prove to all those doubting him that he is still capable of inspiring the side to the title once again.