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Benoit Assou-Ekotto carried the load at left-back for much of last season, but he will need more cover so as to lessen the concern of an injury to him.
Tottenham do still possess the core of a talented and relatively strong squad, but in addition to adding more men up front, some other positions need reinforcement to provide the cover that was lacking at times last season.
Defence is a primary concern.
A good quality centre-back should be enough in that position, with the returning Michael Dawson (injury) and Steven Caulker (an impressive loan spell at Swansea City) along with Younes Kaboul and William Gallas making for good numbers there (even if, as likely, Ledley King does not return).
Full-back is a different matter, with one of the perplexing situations of the last campaign being how Redknapp allowed so many right-backs out on loan, with just Kyle Walker to use until the conclusion of the football league season saw some loanees return.
Spurs were similarly weak at left-back, with Danny Rose and Gareth Bale the only cover for Benoit Assou-Ekotto, both having question marks over their quality in the position should the Cameroonian have suffered a long-term injury.
Failure to reinforce here for this season would leave the Spurs defence once more ill-equipped.
The new manager must quickly decide whether the youngsters like Rose, Adam Smith and Kyle Naughton are good enough here, and if not, new blood will be needed.
The same can be said of attacking midfield positions, where the promising Andros Townsend and the formerly out-of-favor Giovani Dos Santos are two of Spurs' only options left now that Niko Kranjcar has departed.
When fit, Van der Vaart, Bale and Aaron Lennon are all extremely effective. But more often than not last season, at least one was out of action, leaving a gaping absence in the team.
At least one top recruit would be beneficial to help here (maybe more depending on whether one or more of the aforementioned leave), though given the chance, Townsend and Dos Santos could be valuable contributors.