Despite the name this old Hardy's Brewery pub was in Hulme rather than Old Trafford. It was on the corner of Stretford Road and Erskine Road and is shown at the Manchester Archive flickr site in 1962, with a rather addled looking bearded gent outside pointing. He was probably pointing at a fellow drinker from the Platford, as this stood over Erskine Road from the Old Trafford Inn. Indeed, the Talbot and still open Three Legs of Man are right nearby so this must have been a convenient little four-pub-hop when all were still trading. The Old Trafford Arms was the first to close in 1968  (suppose a betting shop and off licence is a reasonable replacement for a pub).
Three Legs of Man, former Old Trafford Inn, Platford, Talbot, Stretford Road. (c) googlemaps.
1. The Old Pubs of Hulme and Chorlton-on-Medlock, Bob Potts (1997).