There is just one known reference for this pub – 13th of April 1838.
‘To be Sold by Auction
All that messuage with brewhouse, outbuildings, Yard & appurtenances there to belonging.
Situate in Talbot Lane Leicester aforesaid, now used as a public house and called the Hope & Anchor in the occupation of Mr E. L. Lockwood.
The fact that the advertisement used the word ‘now’ as a public house indicates it was only used recently, so it could have been a very short lived affair. No mention by 1840.
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Could it have become the Green Dragon? From that pub’s demolition photo it appears to be an eighteenth or early nineteenth building but with apparently no mentions until 1860.
Good shout Phil,the Green Dragon building is certainly older than its licensed records suggest, there is a Green Dragon listed in 1726 but no address, so could be the Market Place one, also a Hope, again no address, so more research to be done, cheers