“Hope is a lover's staff; walk hence with that And manage it against despairing thoughts.”
Proteus describes hope as a walking staff for a lover who has been forced away from the person he loves: it offers something to lean on while facing separation. His advice is complicated by his own disloyalty to Valentine.
Source details
The Two Gentlemen of Verona, Act III, Scene 1: Proteus speaks to Valentine after the Duke banishes him. Although the words sound encouraging in isolation, Proteus has secretly betrayed Valentine’s plan. The MIT play transcription supplies the displayed public-domain wording and scene; this is fictional dialogue rather than Shakespeare’s personal confession.