You are correct in assuming the steerer is already in place and this does not need to change however the crown race (bit that goes on the steerer tube and contacts the bearings inside the headset is unique for each manufacturer of headset)for Hope headset’s they only produce 2 crown races 1 that is for 1 1/8 steerer’s & berings and a second that is for 1.5 steerer’s & bearings. They do not produce a crown race that will allow you to directly put a 1 1/8 steerer into a 1.5 headset.
That is where the adapter I linked to above comes in.
I would suggest partially removing the forks from the bike to have a look at the lower crown race that is fitted. If it looks like the one on the left in the link below you will need the adapter above.
http://www.solidbikes.de/en/product/8?info=1228&xe854b=e4a085c3b3ccbab8b5f8d26e7f98e369
If you are getting it done in a shop give them a call and have a chat, they may have got this part in for you already knowing you will need it.