How does an import quota affect the demand / supply of currency? An import quota in an open economy might not have the desired affect of increasing the GDP as it increases the demand of domestic currency in the open market raising exchange rate. How does it happen that import quota causes demand to shift positively ?
The goal of import quotas is to get people to buy domestic goods, which can only be bought for local currency. Therefore import quotas increase demand for local currency. But...

Setting import quotas is a very undesirable economic policy. It is basically a state intrusion into a market economy. Quotas for imports are usually implemented as a desperate measure when there is a continuously negative trade balance, local currency rapidly loses value, and every other measure (increasing taxes, customs, subsidizing exporters, etc.) failed. Distribution of quotas usually involves plenty of corruption. On top of that, World Trade Organization does not normally allow import quotas. 

The more common use of import quotas is in agriculture, to support local farmers or production of a certain crop. But such limited use of import quotas should have very limited effect on the currency, unless it is a 'banana republic' where agriculture is the main economic activity.