R Yair Spolter and R Shraga Simmons discuss such a case in their series of lessons of blessings (here) and answer one does not need a new blessing.
A bracha includes whatever foods you intended to eat at the time you
said the bracha. [...] What if you had no specific intent? [...] It
depends. In certain situations we assume that – even though you had no
explicit intention – your mind is also on other foods; therefore they
are included in the original bracha and do not require a bracha of
their own. [The conditions for this to be true are]
- More of same food
- Food in front of you
- Some of the original food remains [and you eat more food of the same type]
Your case is the last one
If you say a bracha on a bowl of pretzels, for example, and before the
pretzels are finished you bring out (or decide that you're going to
eat) another food that requires the same bracha – e.g. crackers – no
bracha is required on the crackers. This is because it is normal for
someone who is snacking to start with one food and move on to the
next. Therefore, it is considered as if your mind was on the second
item already when you made the bracha.
Once the original food is finished, however, we assume that you have
decided to terminate the eating session, which automatically ends the
bracha's effectiveness. And any new food brought out at that point
would require a new bracha.
See the original for details and further sources as well as this.