You can determine the common values between the two cell arrays with intersect. In the code below I combine columns Name and Grp both for both "tables" and compare them. The common values between the two are eliminated from PreviousTable, which is then appended to CurrentTable.
Your two cell array inputs:
PreviousTable:
PreviousTable = {'Time','Name','Grp','Rank','Index','Attribute';
'2018-01-03 12:34:00' , 'A' , 'N' , 21 , 2 , 'Good';
'2018-03-23 20:04:12' , 'V' , 'H' , 21 , 11 ,'Good';
'2018-05-17 13:56:00' , 'P' , 'B' , 21 , 11 ,'Good'};
CurrentTable:
CurrentTable = {'Time','Name','Grp','Rank','Index','Attribute';
'2018-05-17 13:56:00' , 'P' , 'B' , 21 , 11 , 'Good';
'2018-04-17 13:56:00' , 'P' , 'Q' , 21 , 11 , 'Good';
'2018-06-05 13:56:00' , 'N' , 'S' , 21 , 11 , 'Good'};
%Find common values between arrays (C) and corresponding indexes (ia).
[C,ia,~] =
intersect(cell2mat(PreviousTable(2:end,2:3)),cell2mat(CurrentTable(2:end,2:3)),'rows','stable');
%Delete redundant rows from first cell array.
PreviousTable(ia+1,:) = [];
%Append PreviousTable to CurrentTable.
CurrentTable = [CurrentTable;PreviousTable(2:end,:)];
Output of CurrentTable:
{'Time' } {'Name'} {'Grp'} {'Rank'} {'Index'} {'Attribute'}
{'2018-05-17 13:5…'} {'P' } {'B' } {[ 21]} {[ 11]} {'Good' }
{'2018-04-17 13:5…'} {'P' } {'Q' } {[ 21]} {[ 11]} {'Good' }
{'2018-06-05 13:5…'} {'N' } {'S' } {[ 21]} {[ 11]} {'Good' }
{'2018-01-03 12:3…'} {'A' } {'N' } {[ 21]} {[ 2]} {'Good' }
{'2018-03-23 20:0…'} {'V' } {'H' } {[ 21]} {[ 11]} {'Good' }
