The best way to fix that is to have the verge tiles removed the old cement raked out and then have the tiles re bedded on to new cement.
Roof verge mortar repair.
Rebedding roof verges by making necessary repairments a cement mortar is known as roof bedding.
The repair specification included for stripping off the large format interlocking concrete tiles at the verges renewing the fibre cement undercloak and cutting out and replacing tantalised roof batten ends affected by wet rot.
Tiles on the verge are often mortared to prevent rain and wind from getting underneath the tiles.
Bear in mind that as time will pass the bedding will gradually wear out.
Dry fix options for verges are also available from a number of manufacturers.
I used this mix because as a complete roofing novice i happened on to this site.
Repair small cracks small cracks in the mortar of the verge can be quickly and easily fixed by using a roof and gutter sealant.
This is injected into the crack with the applicator and allowed to dry before being painted over if required.
Scoop some mortar into an old bucket and use a trowel and mortarboard to apply it on areas where the old mortar was removed.
Use the trowel to butter and smooth the mortar make sure it is even and leveled.
Be careful when lifting mortar to the top part of the roof if it is possible get an extra hand.
You can buy sealant in several colours to match the mortar if it is to be left unpainted.
Over four years ago i repaired about two metres of roof verge using a mix of 4 sharp sand to one of cement.
Sand and cement being the only materials apart from the odd tile if any are broken on removal its not a big job and done correctly you should not have any problems for quite a while.