Servant emptied heaviest containers brought round to supply what's lacking (4,3,3)

'supply what's lacking' is the definition.
(to stop the gap is temporarily address a shortage)

'servant emptied heaviest containers brought round' is the wordplay.
'servant' becomes 'page' (a royal servant).
'emptied' suggests removing the centre.
'containers' becomes 'pots' (pot is a kind of container).
'brought round' is a reversal indicator.
'heaviest' with its middle removed is 'ht'.
'page'+'ht'+'pots'='pagehtpots'
'pagehtpots' reversed gives 'STOP THE GAP'.

'to' is the link.