They should pick a leader who actually supported the Leave campaign, unlike May.
Considering the election result that they had even when they managed to hoover up most of the UKIP vote (by basically stealing the entirety of the UKIP manifesto bar the obviously loathsome bits); this doesn't seem like the most sensible route to take if you'd actually want them to win an election - I'd be all for it though!
The problem that they have is something that the referendum and the General Election have exposed to the world: the Tories are an incredibly divided party, but those divisions are both deep and very irrational - in that the policy divisions for them seem to be... nonexistent, but that they rip the party enough. The issue electorate-wise is that they need to get back the socially liberal softly-remain voters that they lost this year without pissing off the Kippers, and its going to be a struggle to find a leader with the policies that can do that whilst uniting the parliamentary party - May was supposed to be the person that could do that, and look how that's worked out. As Brexit becomes less salient they'll fade away is visibility but not go away in their entirety - after all; Europe will always remain an issue within the Conservative party...
There's also the fact that the places that they seem to have gained votes (and indeed, the places that they targeted in the last General Election although part of that was just Clinton-esque arrogance) are all places that are mostly safely Labour so an increase in the Tory share isn't overly useful unless they start winning 1997-style landslides: while Labour have made much stronger games in other places (in London and the South especially - the Labour numbers amongst younger voters also should terrify the Tories, since 70% of 18-25 year olds voting Labour suggests that there's lots of young Labour voters from rich families, which isn't something that's ever really happened before to this extent) that have helped them win seats now - Labour gained Canterbury, have made traditional Tory seats in places like Worthing competitive in a good year for them, and have made places like Birmingham Edgbaston, Bristol West and Hove (all Tory and comfortably so in 1992; to the point where in 1997 Labour winning them all was a surprise - sure lots of this is demographic changes and boundary changes in the case of Bristol West but even then, Labour having a 20,000 majority in Hove in a seat the Tories had in 2010 shows the problem that the modern Tory party have to face.
I don't think the problem is moderation - after all; Cameron stood on a distinctly not moderate economic platform in 2015; and Jeremy Corbyn led Labour to their best vote share since 2001 and highest number of votes since 1997 - but more the perception that your party and leader cares about people - I'd argue that's fundamentally the main difference between the Tories of 2015 and those of 2017, and a big thing as to how Labour managed to get votes even from people that were concerned about how radical they perceived them to be.
