Why is there no salt bridge for hydrogen–silver bromide cell?
The function of a salt bridge or a diaphragm is to avoid mixing of 2 different electrolytes or electrolysis products from the respective half-cells, while allowing ion electro-migration between them.
This cell does not need a salt bridge as it uses the only electrolyte $\ce{HBr(aq)}$ and the is no need to separate the $\mathrm{AgBr}$ electrode from gaseous hydrogen.