#1 Invest smartly in the Transfer Market
He has been popularly referred to as the Martyr of Islington and was for a long time rightly revered for his brilliance in playing the market but Wenger's last few years have been disappointing when it comes to player recruitment.
The genius who routinely picked up good/struggling players for bargains, turned them into brilliant performers (and sometimes sold them for crazy profits) has not been seen for a while. Instead, there has been a scatter-gun approach to player recruitment with core areas which are in need of reinforcement being left alone while areas that already had quality are reinforced (the purchase of Pierre-Emerick Aubameyang mere months after the arrival of Alexandre Lacazette a case in point).
Until the signing of Mesut Özil from Real Madrid in 2013 for £42.4m, Wenger had been steadfast in his refusal to pay top money/salaries for stellar talent, an attitude that, while principled, saw the Gunners lose out on lots of top rated talent who could have helped the team immensely.
This is one example the new manager cannot afford to follow as football is now an arms race and spending wisely like Manchester City did this season is one of the surest ways of winning titles.
The board will also need to give him full backing and given the Gunners' finances, this should not be a problem.