In the same way that you can combine QSOs you have made using different personal callsigns from the same DXCC country for DXCC purposes e.g. if you have upgraded to a new license class and call, or if you hold a vanity call or contest call for your personal use (not a club call), you can combine or "link" your personal callsigns in Club Log.
Linking is under the Settings option at the top of the page, so long as you are logged-in to Club Log.
Linking means that the DXCC scores for your primary callsign will include the linked callsigns' logs. Linking is indicated on the league tables with, for example, "+1": the number indicates how many other callsigns are linked to that primary call. Click the callsign to find out which other calls are linked to it.
See: http://clublog.freshdesk.com/solution/articles/53188-how-do-i-link-my for more information.