Assuming that the door has been correctly installed in the first place and has a load bearing lintel above it then you shouldn't need to install anything extra to support the brickwork. The joinery which you are removing is simply to attach the door to the wall and make it look nice.
Of course if the door was installed by cowboys or it is an exceptionally of property there may be no lintel which is outside my comfort zone, if you're not certain I'm sure you'll be aware that getting a structural engineer in can save money in the long term.
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