Without knowing the error message it is difficult to even guess - it may be as simple as you have a field name wrong.
But please, please, please do not concatenate strings to form an SQL command! It leaves you wide open to accidental or deliberate SQL Injection attack which can destroy your entire database. Use Parametrized queries instead:
string sqlInsert = @"INSERT INTO clients(Client, Contact, Address, Telephone, NumberOfJobs, LastJob)VALUES(@CL, @CN, @AD, @TN, @JC, @LJ)";
try
{
conn.Open();
SqlCommand cmd = new SqlCommand(sqlInsert);
cmd.Parameters.AddWithValues("@CL", this.Client);
cmd.Parameters.AddWithValues("@CN", this.Contact);
cmd.Parameters.AddWithValues("@AD", this.Address);
cmd.Parameters.AddWithValues("@TN", this.Telephone);
cmd.Parameters.AddWithValues("@JC", this.NumberOfJobs);
cmd.Parameters.AddWithValues("@LJ", this.LastJob);
cmd.ExecuteNonQuery();
And it is a lot easier to read!