Bailey has assumed direct responsibility for the division, which counts 240 regional newspapers, until further notice.
Parker, who spent 20 years at Trinity Mirror, is currently serving a 12-month stint as president of the Newspaper Society.
Parker's departure follows that in June of Norman Walker, managing director of Mirror Colour Print, who had served 23 years at the firm.
Walker has effectively been replaced by group director of manufacturing Rupert Middleton, who joined in March, whose remit is to cut printing costs across the group's 12 print sites.
An update on Middleton's findings will be published on Thursday (29 July) as part of Trinity Mirror's report on its interim results.
Story by Josh Brooks