If you go up from the Globe, just after The Slug & Lettuce, is The Vestry.
It can be a bit pricey as it's chock full of continental speciality beers and LOCAL ales.
The last time I was in I was supping a reasonably priced Dark Star.
(As we were drinking in rounds and 'loadsamoney' was in the chair, a mate ordered some £6.00 a pint Belgium beer )
Told by a pompey mate that The Good Companions is a friendly pub that welcomes home and away without hassle, on the way in Eastern Road I think just to the east of the ground. Thats where we are heading