The current version of the school crest as found on the website and on blazers is a kind of blurry version of the one I remember from the 1960s. It no longer carries the motto Discendo Duces, which now, indeed, seems to have disappeared completely.
According to Anthony Tuck ON in his essay 'Towards the Front Rank 1922 - 1945' this coat of arms was adopted in 1930 to replace the tradition followed since the nineteenth century of juxtaposing the arms of Queen Elizabeth I with those of the city. The cost of the grant for the new arms was met by Sir Arthur Sutherland. Discendo Duces ('through learning you will lead') became the school motto the following year apparently replacing Progrediendum Est (which sort of means 'setting out'), although I have not been able to find an example of this.
The new crest and motto were part of an attempt by headmaster Ebenezer Rhys Thomas (1922 - 1948) to reinforce the school's sense of status and pride. The school song also dates from this period.
Prior to the nineteenth century the school seems to have simply used the arms of the city.