Yes, it is possible that you will need planning permission.
Generally speaking, planning permission will be required for the erection of a new sign on business premises. The Land Planning and Development (Guernsey) Law 2005 provides that planning permission will be required for "attaching to or painting or otherwise exhibiting on the exterior of any structure, or placing on land, an advertisement or sign".
The main reasoning behind this is to ensure that signs are appropriate and to ensure they do not spoil the character of the environment. It is recognised that signs and advertising are an important way of promoting business and services and signs that are carefully designed, may enhance the quality of our surroundings. Badly designed signs and those that are too big, badly located, or inappropriately lit, can undermine the quality of a place.
There are some "exemptions" where planning permission will not be required, but it should be noted that most of the exemptions do not apply to protected buildings or monuments.
The exemptions are set out in full in the Land Planning and Development (Exemptions) Ordinance 2007 and they cover things like contractors' signs (temporary signs where contractors are engaged in building or other works) and nameplates identifying any individual, company or firm carrying on a trade, business or profession from that building (subject to compliance with certain criteria).
If you are repainting or replacing an existing sign, provided that the sign, as repainted/replaced, is not internally illuminated and the overall size and location is not changed, planning permission will not be required (unless the sign is on a protected building or a protected monument).
If your proposed sign does not fit within one of the exemptions set out in the Exemptions Ordinance, you will need to obtain planning permission and if you are unsure, you should always seek professional advice.