Reverse universal motor from a sewing machine
Summary:

Disconnect the wires from the two brushes.

Reconnect the wires to the brushes that they were not connected to before.
(A little extra wire will probably be required).

Done.



Universal motors are what is known as &quot;series wound&quot; - they have the whole motor current flowing in series in both the field coils and the armature.
When the AC supply reverses the current flow to both field and armature also reverse so the same relative polarity is maintained.
To reverse the motor direction you thus either need to swap the wires to either the brushes or to the field (but not to both).  eg
Wire previously going to brush A now goes to brush B.
Wire previously going to brush B now goes to brush A.
There is a chance that the motor is designed mechanically to work better one way than the other but if there is no prospect in using the motor as supplied reversal may still be acceptable.

As @BrianDrummond notes -

in some cases brush holders are adjustable in rotational position over a small range. Adjusting the position [with due care to avoid electric shock] can optimise the position and reduce commutator sparking.

Brushes optimised in position for one direction of rotation may be slightly off position in reverse.
As @Charles Cowie notes -

&quot;If the brush mounting assembly has a lot of room to rotate, and if the wires are long enough, you may be able to reverse the motor by turning the mounting assembly 180 degrees.&quot;

This is electrically the same as swapping brush leads but may be easier.
It's unlikely to be possible in the present case (based on the photo).