Praise be to Allah.
If he owned gold that reached the nisaab (minimum threshold at which zakaah becomes due), then he sold it, or some of it, and used its price to buy trade goods, then the zakaah year is not interrupted, and he must pay zakaah when one year has passed since acquiring the gold.
Al-Kaasaani said in Badaai’i‘ as-Sanaa’i‘ (2/15): If he exchanges trade goods for other trade goods before the zakaah year is completed, the zakaah year is not interrupted, regardless of whether he replaces it with something of the same category or something of another category, and there is no difference of scholarly opinion concerning that. That is because the obligation of giving zakaah on trade goods has to do with the fact that they are wealth; thus they are wealth and have value, so the zakaah year will continue for that reason, and it cannot be interrupted by these exchanges.
The same applies to dirhams and dinars (silver and gold coins, respectively): if a person sells them for the same kind or a different kind, such as selling dirhams for dirhams or dinars for dinars or dinars for dirhams or dirhams for dinars…
So the fact that zakaah is due on dirhams and dinars is also based on the fact that they are wealth, and is not connected to the specific dirhams that he has in his hands, and the description of being wealth remains even after exchanging them. Hence the zakaah year is not interrupted, just like in the case of trade goods.
Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (2/504): When a person exchanges wealth that reached the nisaab for wealth of another kind, then the zakaah year is cancelled, and a new zakaah year begins, except when gold is exchanged for silver or trade goods, because gold and silver are like the same type of wealth, as they may be paid as a penalty for an injury that one causes, or may pay the value of damaged items, and one of them should be put together with the other for the purpose of giving zakaah.
Similarly, if he buys trade goods with currency that reached the nisaab, or he sells trade goods and the money he receives reaches the nisaab, the counting of the zakaah year is not interrupted, because zakaah is due on the value of the trade goods, not on the goods themselves, and the value is worked out in currency. Therefore they fall into the same category of wealth. End quote.
Similarly, modern forms of currency, along with gold, silver and trade goods are all regarded as one category of wealth.
Based on that, if you bought the shares for the purpose of trading them, then they are trade goods, and in Ramadan – which in your case is the completion of the zakaah year for the gold – you must look at the market value of these shares, add it to the gold that you still have and give zakaah.
But if you bought the shares with the intention of keeping them and benefitting from their income, then in this case zakaah is subject to further discussion. Based on that discussion, the decision may be made as to whether the zakaah year for the gold is cancelled or not.
If someone buys shares with the intention of benefitting from their income, without trading in them, then zakaah is due on the income only, unless the shares have to do with something that is subject to zakaah, such as gold, silver, crops and fruits, or currency, in which case zakaah must be paid.
In this case, if there is no currency or gold or silver represented in the shares, then the zakaah year for the gold is cancelled, because the nisaab of the zakaah was changed to wealth of a different type.
But if the shares represent some money or gold or silver, then the value of that gold is represented in the shares, so the zakaah year is not cancelled. To be on the safe side in this case, you should pay zakaah on the shares when the zakaah year for the original gold is completed, that you sold and bought these shares with its price.
And Allah knows best.