Daily entries from the 17th century London diary
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A gallery to which Lord Sandwich, Messrs. Creed and Pepys walked from the Park at Whitehall Palace, and from which they then walked more in White Hall garden, 30 June 1663.
A read of the map of Whitehall Palace shows no Gallery near the Park
http://www.londonancestor.com/maps/whitehall-palace.htm
Perhaps the Gallery in question is the Stone Gallery which is near the garden http://www.pepysdiary.com/p/6076.php
Or the Matted Gallery one floor above it.
http://www.pepysdiary.com/p/5840.php