IS IT POSSIBLE TO DETERMINE THE NATURE OF CHARGE OF AN OBJECT THROUGH A GOLD LEAF ELECTROSCOPE?

Yes we can do that
For that we need a charged electroscope, say it’s positively charged
The leaves would be some distance apart
1) Unknown object is positively charged
we bring close that object then by induction -ve charge will be more on the top of electroscope and to compensate that the +ve charge is more on the leaves and hence their separation would increase

2) If negatively charged
Exact opposite of 1 will occur and the leaves will come closer