The committee was hearing evidence on the governance and culture of Parc, and members were told safety at the prison had improved.
There have been 17 inmate deaths on the estate this year and several prison staff have been arrested on suspicion of assault and misconduct in public office.
Mr Brockington said eight of these were declared natural causes of deaths, three were self-inflicted and five were believed to be drug-related.
Parc had an ageing population, he added, with 16% of prisoners over the age of 50, and was one of two palliative care centres.
He said another "significant issue" was the introduction of nitazenes - a type of synthetic opioid - into the prison in the first half of the year.
"These are drugs that are up to 1,000 times more powerful than morphine."
Ruth Jones, the committee chair and Labour MP for Newport West and Islwyn, asked if the prison could guarantee inmates were safe.
Mr Styles said "an awful lot of work" had been done to improve safety and security.
"I think we've made really significant progress in improving safety outcomes," he said.
"Certainly when we look at measures including self-harm and violence the metrics have improved very significantly."
There had not been a non-natural death at the prison since June, he added.
"The feedback from the men is also that things are improving in terms of conditions for them, in terms of the regime and in terms of safety."