Not until level 18
Wildshape's 3rd bullet point is quite clear:
You can't cast spells [....]
A druid that shifts into Wildshape can't cast any spells, regardless of their VSM components. This includes spells from innate spell slots, scrolls, and other magic items which state that they enable the wielder to cast a spell. A DM may choose to ignore this rule, but as written, the form of a druid's Wildshape has no bearing on its ability to cast a spell.
This changes later on. At level 18, Druids get the Beast Spells feature:
Beginning at 18th level, you can cast many of your druid spells in any shape you assume using Wild Shape. You can perform the somatic and verbal components of a druid spell while in a beast shape, but you aren't able to provide material components.
This allows any/all Druid Wildshape forms to cast V, S, or VS spells. A Druid still doesn't get to cast spells with a material component until level 20:
[...] Additionally, you can ignore the verbal and somatic components of your druid spells, as well as any material components that lack a cost and aren't consumed by a spell. You gain this benefit in both your normal shape and your beast shape from Wild Shape.
So, finally, at level 20, a Druid may be an ape or (or other beast) and cast a spell that has a material component, so long as that material doesn't have a cost associated with it and isn't consumed by the casting of the spell (the spell would indicate if either of these were the case).