Mr Brewster, 29, died of stab wounds in the Llanedeyrn area of the city on Sunday, 12 June.
Robert Lainsbury, 22, originally from Kidderminster, has been charged with his murder along with Dwayne Edgar, 29 from Llanedeyrn.
Police now want to speak to Jake Whelan, 23, also from Kidderminster.
Mr Whelan is known to have links in Cardiff and is understood to work as a personal trainer, so might be known to gym users in Kidderminster and Cardiff, said police.
The public are advised not to approach Mr Whelan directly, but to call police immediately if they have any information about his whereabouts.
Two other men from Cardiff, aged 19 and 35, who were arrested in connection with the death have been released on police bail.
A second man has been charged with the murder of Lynford Brewster in Cardiff and police are appealing for a third man to come forward.